报告时间：2023年3月16日（星期四）15:00

报告地点：翡翠科教楼B1710

报 告 人：欧阳毅 教授

工作单位：中国科学技术大学

举办单位：威尼斯官网

报告简介：

Suppose K is a global field, L/K is a cyclic extension and A/K is an abelian variety. In this talk, we prove several unboundedness results of the Tate-Shafarevich groups Sha(A/L) under the conditions that:

(1) A is a fixed abelian variety over K and L varies over cyclic extensions of K of the same degree, which give an affirmative answer to an open problem proposed by K. Cesnavicius;

(2) L/K is a fixed cyclic extension, and either K is a number field and A varies over elliptic curves，or the degree of L/K is 2-power and A varies over quadratic twists of a principally polarized abelian variety, which generalize results of K. Matsuno and M. Yu respectively.

This is a joint work with Jianfeng Xie.

报告人简介：

欧阳毅，中国科学技术大学数学系教授，博士生导师。中国科大学士（1993）、硕士（1995），美国明尼苏达大学博士（2000）。毕业后在加拿大多伦多大学和清华大学工作，2006年回中国科大任教授。主要研究方向为代数数论和算术代数几何。2018年被评为安徽省教学名师，并荣获2017年宝钢优秀教师奖和2022年霍英东教育教学奖等荣誉。发表SCI论文40余篇，包括国际著名数学期刊Crelle和Compositio Math,等，并与国际著名数学家Fontaine、Benois完成论著Theory of p-adic Galois representations。